A spherical coordinates was built, whose origin is at the top of the cone tangent to the container at the contact line of the meniscus with the container wall. The velocity potential and the liquid surface displacement were determined analytically in terms of the Gauss hypergeometric series. The variational principle was transformed into a frequency equation in the form of a standard eigenvalue problem by the Galerkin method. The first eigenfrequency solved by this method was compared with that from other theoretical and experimental methods. Large calculations prove that this method is effective in solving the small amplitude sloshing eigenfrequency of liquid.